Fresnel aspheric lens

ABSTRACT

An aspheric lens is made with a fresnel type aspheric curvature on at least a portion of its back surface and with the aspheric curvature being defined in the X-Y coordiante system by a particular relationship in accordance with the index of refraction, heighth, focal distance and radius of back surface parameters.

United States Schaefer Continuation of Ser. No 36880, May 13, 1970,abandoned, which is a continuation-in-part of Ser. No. 25,179, April 2.1970, Pat. No. 3,708,221.

Assignee:

(1.5. CI 350/189, 240/1061, 350/211 Int. Cl G02b 3/04, G02b 3/08, F21r5/04 Field of Search 350/178, 189, 190,

is: July 3, 1973 [56] References Clted UNITED STATES PATENTS 1,955,5994/1934 Lamblin-Parent 240/1061 Primary Examiner-Ronald L. WibertAssistant Examiner-Paul A. Sacher Attorney-Arthur G. Connolly et a1.

[5 7] ABSTRACT An aspheric lens is made with a fresnel type asphericcurvature on at least a portion of its back surface and with theaspheric curvature being defined in the X-Y coordiante system by aparticular relationship in accordance with the index of refraction,heighth, focal distance and radius of back surface parameters.

9 Claims, 12 Drawing Figures PMENIEDJIIL -3 I73 mun FRESNEL ASPIIERICLENS CROSS-REFERENCE TO RELATED APPLICATION This application is acontinuation of application Ser. No. 36,880, filed May 13, I970, and nowabandoned which in turn is a continuation-in-part of copendingapplication Ser. No. 25,179; filed Apr. 2, 1970 now US. Pat. No.3,708,221.

BACKGROUND OF INVENTION Aspheric lenses have been utilized in the priorart for various purposes. As pointed out in the parent application adifficulty with the prior art lenses has been in the accurate forming ofthe aspheric curvature. The parent application disclosed a means whichrepresented a significant breakthrough in attaining a high degree ofaccuracy and control over the specific aspheric curvature and which haslent itself to mass producing high quality products.

The disclosure of the parent application was primarily directed to awide variety of aspheric lenses wherein the aspheric curvature wasformed on the frontal surface. Although the lenses were intended for alarge number of different uses there was particular utility in theapplication of these lenses in motor vehicle systerns.

SUMMARY OF INVENTION An object of this invention is to provide anaspheric lens which utilizes the concepts of the parent application toobtain even greater versatility thereof.

A further object of this invention is to provide such an aspheric lenswhich has particular utilization in a vehicle headlight system tominimize glare to the oncoming driver.

A still further object of this invention is to provide a modifiedaspheric lens which has applicability for producing the intendedconcentrated parallel rays of light regardless of the environment of thelens.

A still further object of this invention is to provide a lens of thetype which is equally effective in air or under water.

In accordance with one aspect of this invention an aspheric lens of thetype described in the parent application is provided wherein an asphericcurvature is created on the frontal surface to create the concentratedrays of light having minimal chromatic aberrations and wherein the backsurface includes parallel spherical segmental flutes to create auxiliaryspread light and also includes fresnel-type flutes to prevent the spreadlight from being directed into the eyes of the oncoming driver. Thefresnel-type flutes are in the form of an aspheric curvature.

In accordance with another aspect of this invention the lens is formedwith a planar frontal surface and with a fresnel-type aspheric curvatureon the back surface. This lens creates a concentrated light beam ofparallel rays having minimal chromatic aberrations regardless of theenvironment of the lens and is thus equally useful in water, air andother environments.

As is apparent hereinafter the aspheric curvature is a smooth curve ofconstantly changing radius with the point constantly recalculated inaccordance with certain parameters to uniformly distribute the light, incontrast to an aspheric hyperboloid which concentrates the lightaxially.

THE DRAWINGS FIG. 1 is a side elevation view of a convexo-aspheric lensof the type described in the parent application and schematicallyincorporated in a vehicle headlight system;

FIG. 2 is a schematic showing of the various parameters utilized indetermining the specific aspheric curvature;

FIGS. 3-4 are front and rear elevation views of a fluted piano-asphericlens of the type described in the parent application;

FIG. 5 is a cross-sectional view taken through FIG. 4 along the line 5-5and showing the ray trace thereof;

FIG. 6 is a schematic illustration of the parameters used forcalculating the flute spread in accordance with this invention;

FIGS. 7-8 are front and rear elevation views of a fluted plano-asphericlens in accordance with this invention;

FIG. 9 is a cross-sectional view taken through FIG. 8 along the line 9-9and showing a ray trace thereof;

FIGS. 10-11 are front and rear elevation views of a further form ofaspheric lens in accordance with this invention; and

FIG. 12. is a cross-sectional view taken through FIG. 11 along the line12-12 and showing the ray trace thereof. 1

DETAILED DESCRIPTION To appreciate an understanding of the developmentof this invention reference made to the techniques described in parentapplication Ser. No. 25,179; filed Apr. 2, 1970, the details of whichare incorporated herein by reference thereto.

As described in the parent application the basic concept of the novelaspheric curvature begins with a lens 10 having an aspheric frontalcurvature l2 and a convex back surface 14 which is in the segment of asphere. A peripheral rim l6 adapts the lens 10 to be mounted in avehicle headlight system which may include for example a housing 18having any suitable point source of light which may be simulated byutilizing light source f, and an elipitical reflector 20 to refocus thelight rays 22 to infinity with minimum chromatic aberration. Asschematically illustrated in FIG. 1 lens 10 closes the open end of thehousing 18. Housing 18 also includes an aperture plate 24 having itsaperture at the focal point f, with lens 10 being symetrically arrangedon the optical axis 26 of the headlight system. The paths of lightpassing through lens 10 are parallel to the optical axis 26 to anunusually high degree of accuracy thereby producing a highlyconcentrated light beam which is particularly effective for lighting aroadway. The housing 18 and its various components are connected in theheadlight system as an auxiliary light or as a replacement for eitherthe conventional high or low beams. Any suitable glass composition suchas a borosilicate glass may be utilized with this invention whilestillattaining the high degree of accuracy. It is to be understood, ofcourse, that although the lens 10 is described with particular referenceto use in a vehicle other uses are also possible within the scope ofthis invention where there is a requirement for a concentrated lightbeam having minimal chromatic aberration and wherein the paths in thelight beam are parallel to the optical axis.

As described in the parent application, frontal surface 12 is formedwith an aspheric curvature which may be accurately reproduced andcontrolled through a series of mathematical calculations whichparticularly lend themselves to the use of computer techniques therebyvastly reducing the time and labor requirements. The formulas used fordetermining the aspheric curvature are particularly noteworthy in thatthe many parameters canbe varied while still producing a highly accuraterelatively low cost mass produced lens with very good light controlproperties. The parameters which can be varied in accordance with thisinvention are the radius of back curve, the focal distance to the faceof the back curve, the refractive index of the glass, the diameter ofthe lens and the thickness of the lens.

FIG. 2 schematically illustrated the various parameters which must beconsidered in forming the lens 10 and which are taken into account inaccurately producing and reproducing the aspheric curvature on thefrontal surface 12. As is readily apparent in FIG. 2 the asphericcurvature is a smooth curve with constantly changing radius. Asindicated in FIG. 2 the focal point FP lies upon the optical axis 26.This axis is also designated as the XX axis of the X-Y coordinatesystem. Where the optical axis intersects the face of the back curve ofthe convex back surface and tangent thereto is the Y-Y axis of the X-Ycoordinate system. The heighth of the ray of light is indicated as H,and corresponds to the Y- distance at which the ray of light intersectsthe Y axis. The various points on the aspheric frontal surface 12 eachhave a corresponding X and Y value in accordance with the X-Y coordinatesystem. As later used in the formulas for defining this curvature theseX and Y values are indicated as X, and Y, which represents the variableX and Y coordinates. The maximum thickness of the lens is illustrated inFIG. 2 as T, while F, represents the focal distance of thefocal point FPto the back surface of the lens. K, designates the limit of activesurface. It is not necessary to continue the aspheric curvature beyondK, and thus the remaining portion 16 of the frontal surface may be usedfor mounting the lens 10 in any suitable housing. The lower computerlimit of the X value of K, is indicated as L, while the upper limit isdesignated as L,. The radius of the convex back surface is designated asR,.

The various points on the aspheric curvature are defined in the X-Ycoordinate system by the variable B, being equal to {X,[COT(A,,) +Y,-J,D,[TAN(A,) l /[TAN(A,) COT(A,,)] and the corresponding C, being equal toJ, (B,D,) [TAN(A,) These formulas represent a shorthand method ofcomputing the aspheric curvature and the designations therein arederived from the following mathematical calculations wherein N, .is theindex of refraction and other parameters have their designations in FIG.2; B, is the X value of the point being calculated and C, is itscorresponding Y value; and wherein X, is the X value of the previouscalculated point, while Y, is the Y value of the previous calculatedpoint and wherein: G, 4(2 R ,F, F12); 1 ATN a/ 1); 1 i' 1)'[ i)]; 2 1 t;5 2 1 1 5[ l) l; D! r-' [TAN(AI)I;AZ ASN r/ 1); 1 1+ 1; 1)/ I]; 4 A A,ATN {SIN(A,)/[ N, COS(A,) 1}; and A, A, A,

In the practical application of these formulas, rough limits L, and L,are set upfor computer usage which in turn sets up rough limits thatconfine the point K, as far as X values are concerned. This locates thelimits that the X value of K, must fall within, in relation to the X-Yaxis intersection located tangent to the back spherical radius. Then thecomputer is made to refine the calculated curve by use of the finelimits L, and L which tie down the X value of point K, to any degree ofprecision desired.

It is understood that for any particular computer run, other variableparameters such as R,, F,, N,, T, are given numerical values. Thisprocess of calculation of aspheric curves allows one to choose an N,(Index of Refraction) of a commercially available glass for the designof aspheric lens with a high degree of accuracy that can be massproduced from conventional glasses.

By utilizing conventional computer techniques and selecting an Xdimension with sufficient significant numbers it is, therefore, possibleto quickly obtain an unusually high degree of accuracy of for example l0with respect to the emitted rays of light being parallel to the opticalaxis. It is even possible through computer techniques with the inventivemanner of forming the aspheric curvature to obtain a degree of accuracyas fine as 10 While the lens illustrated in FIGS. 1-2 is highlysatisfactory for producing the desired concentrated rays of light, theparent application points out a further development which isparticularly adapted for use in a vehicle headlight system by creatingan auxiliary less concentrated light spread. This auxiliary light spreadis, in general, created by the inclusion of parallel flutes on the backsurface. Each flute has a cross-section in the form of a sphericalsegment.

FIGS. 35 illustrate one form of modified lens. As described in theparent application, this lens is a planoaspheric lens 44 having anaspheric curvature on its frontal surface 12 and a plano back surface 48with a plurality of parallel flutes 46. The planar surface includes acircular area 50 which is free of flutes and which lies on the opticalaxis 26. The resultant ray trace is illustrated in FIG. 5. Asillustrated therein concentrated rays of light 38 are producedsubstantially parallel to the optical axis 26 to thus provide theprimary means of light. The provision of flutes 46 create spread lightas indicated by the rays 40 which are desirable to permit peripherallighting for the driver.-

FIG. 6 illustrates the manner of computing the flute spread. Since theintensity of the light beam is not as critical with the spread light, itis assumed that each flute is symetrically arranged with respect to theoptical axis 26 having its focal point FP lying an the XX axis of an XY-coordinate system. The Y-Y axis is disposed tangential to the fluteouter surface at the intersection of the optical axis and the backsurface thereof. The half heighth of a flute is designated as h, whilethe heighth of cord or maximum distance the flute extends into the lensis designated as h,. Each flute has a cross section which is the segmentofa sphere having a radius indicated as r,. The angle in degrees ofspread is designated in FIG. 6 as a." The flute spread may then becalculated as r, h,/SIN(A,) and h, {r, 0.5 V [4(r (2h,)] wherein a, a1r/360; a, ASN[SIN(a1)/N,]; a, ATN {SIN(a,)/[N, COS (a '1}; a a, a andN, the index of refraction. With the above defined relationship theflutes are formed to provide any specified amount and angular spread ofthe spread light. The parameters that may be varied include the indiciesof refraction, thickness of lens, diameter of lens, focal distance fromFP to the back surface of lens, amount of spread light desired, angularspread desired and width of flutes.

FIGS. 7-9 show a further aspheric lens 72 which is formed in accordancewith this invention. As indicated therein the lens 72, however, includesprovision to create a convergent spread light at the upper portion ofthe lens so that the spread light will not shine into the eyes of theoncoming driver. Thus the planar surface 74 includes two types offlutes. One type of flute is the parallel spherical segmental flute 76which creates a divergent spread light. At the uppermost portion of theplanar back surface, however, fresnel type parallel flutes 78 areprovided. Unlike conventional fresnel lenses, the flutes 78 form incross section, portions of a continuous aspheric curvature, rather thanthe conventional spherical curvature or prism type lens. This asphericcurvature would be formed in accordance with the manner of computing theaspheric curvature described in connection with FIG. 2.

FIGS. 10-12 show another form of this invention which is particularlymeritorious. The lens 80 illus-. trated therein represents a significantdeparture from exiting practices with both fresnel lenses, per se, andwith aspheric lenses. In this respect conventional fresnel lensesincorporate the curvature on the frontal surface while the back surfaceis planar. In such conventional fresnel lenses the curvature isconstructed in the form of spherical steps or risers with the index ofrefraction of the outside environment being taken into account whenforming the curvature to produce to desired ray trace. Whenthe outsideenvironment (and thus also its index of refraction) is changed, the raytrace is also changed. Accordingly, such conventional lenses aredependent on their environment.

Unlike such conventional lenses the lens 80 includes a planar frontalsurface 82 and a fresnel-type back surface 84 wherein the individualsegments comprise portions of an aspheric curvature as previouslydiscussed. By forming the fresnel surface 84 at the rear, the light inthe sealed housing entering the lens 80 is made parallel to the opticalaxis within the lens and remains parallel and uniforrnaly distributedwhen emerging therefrom since the frontal surface 82 is planar. Thisembodiment is particularly advantageous since it renders the emergingpath of light independent of its environment beyond the frontal surface82. Lens 80 is thus equally adapted for use underwater, in air or anyother environment, regardless of the index of refraction of the outsideenvironment. Lens 80 thus would have particular utility for submarineuse, by scuba divers or in swimming pools where it might be desirable tohave a high powered concentrated light beam.

As previously noted the aspheric fresnel-type surface 84 is formed as anaspheric curvature of the type described in conjunction with FIG. 2.Thus the fresnel curvature is based upon the fundamental concepts withrespect to the convexo-aspheric lens of FIGS. 1-2 and also theplane-aspheric lens of FIGS. 3-5. The aspheric lens surface iscalculated in the same manner as previously described with theadditional parameter of a vertical riser (V,) which acts as anartificial restraint for restarting or shifting the aspheric curve aslater described. Additionally, for computer use the aspheric surfacecalculations define X, as the X point on the curve; Y as the Y point onthe curve and Y, as the Y increment. Because of the specificconstruction of lens which includes for example the planar surface 82,the formulas discussed in conjunction with FIG. 2 are simplified intothe following formulas: A, ATN(H- l l), 1)/[ 1 1) 1 I 1 M 3)]HI[COT(AI)I}[TAN(A3) COT(AX) 1, 1 X, (C, Y,)[TAN(A,) X, 8,; and Y, C,.

In the practical application of these formulas the aspheric curvature 84is calculated beginning at the intersection of the optical axis 26 andthe imaginary plane or plane of origin 27 and continues until a limitingdepth equal to the vertical riser V, is reached. The curve then shiftsback to the plane of origin 27 and continues until the limiting depth V,is again reached. This process is repeated until the entire asphericcurvature is formed. Ideally the step or physical shifting from thelimiting depth back to the plane of origin 27 should be perpendicular tothe plane 27. For manufacturing reasons, however, this step, such asindicated by the reference numeral 29, is made slightly inclined. Ithasbeen found that such a deviation from the normal does not introduce anysignificant inaccuracies.

The method of forming the aspheric curvature 84 wherein the curvatureextends to a limiting depth and then shifts back to a plane of originmay also be employed for forming the aspheric curvature 78 of FIGS. 7-9.

What is claimed is:

l. A light transmitting lens comprising a lens body having a frontalsurface and a back surface, said back surface being substantiallyplanar, a plurality of parallel flutes formed in a generally circulararea on said back surface to diverge the rays of light away from theaxis of the lens to thereby create an auxiliary spread light, afresnel-type curvature being disposed in said circular area at the topedge of the active area of the back surface transverse the direction ofsaid parallel flutes to direct the rays of light downward toward theaxis of the lens, said fresnel-type curvature being formed from anaspheric curvature, said aspheric curvature being a smooth curve ofconstantly changing radius said generally circular area is ring shaped,said frontal surface is non-planar and said frontal surface has anaspheric curvature which is a smooth curve with constantly changingradius.

2. A light transmitting lens for a housing having an open end with alight source in the housing disposed remote from the open end, said lenshaving mounting means for closing the open end of said housing from itssurrounding environment, said lens having a back surface for beingdisposed within the housing and a frontal surface for being disposed inthe environment outside the housing, said frontal surface being planar,the entire active area of said back surface having a fresneltypecurvature with concentric ridges, said fresnel-type curvature beingformed from a non-hyperboloid aspheric curvature, and said asphericcurvature being of smooth curve of constantly changing radius with thepoints on the curve being constantly recalculated in accordance with thefocal distance to the face of the back surface, in accordance with theindex of refraction of the lens and in accordance with the verticalriser limiting depth to create a uniform concentrated beam of parallelrays.

3. An aspheric lens as set forth in claim 2 in combination with a lightsource, and said back surface being disposed between said front surfaceand said light source.

4. An aspheric lens as set forth in claim 3 including a housing havingan open end, said lens closing said open end to seal said housing, andsaid light source being in said housing.

5. In an aspheric lens which produces paths of light parallel to itsoptical axis from the rays of light passing therethrough with theemitted light being concentrated and haVing minimal chromaticaberration, said lens having a frontal surface and a back surface, atleast a portion of said back surface having a fresnel-type asphericcurvature; said frontal surface having an aspheric curvature, said backsurface being substantially planar, and a plurality of parallel flutesbeing formed in a portion of said back surface to provide an auxiliaryspread light pattern, said flutes being arranged in a substantially ringshaped area, said fresnel-type curvature being in a portion of saidarea, and said flutes being disposed substantially normal to saidfresnel-type curvature, said aspheric curvature on said frontal surfacebeing defined in the X-Y coordinate system by B, being equal to{X,[COT(A,,) 1+ Y,J, D,[TAN(A,) ]}/[TAN(A,) COT(A,) and C, being equalto J, (B, D,) [TAN(A,) wherein N, is the index of refraction, H, is theheighth, X, is the X value of the previous calculated point, Y, is lvalue of the previous calculated point, F, is the focal distance fromthe focal point to said back surface, R, is the radius of the backsurface, G, 4(2R,F, Ff) A, ATN (H,/F,), E, l l) [COS(AI)]1 E2: E12 la M:(E1 V E2) 1= 5[ 1)l, 1=( 1 1)[ M 01. 1

A, A A A ATN {SIN(A,)/N, COS(A,) 1}, A A, A B, X value of point beingcalculated; and C, Y value of pointbeing calculated.

6. An aspheric lens as set forth in claim 5 wherein sald fresnel-typeaspheric curvature is defined in the same manner as said frontal surfaceaspheric curvature.

7. An aspheric lens as set forth in claim 6 wherein each of said flutesis defined in cross-section by a radius r, h,/SlN(a,) and a chordheighth h, [r, 0.5 V +(r,) (2h,) wherein N, is the index of refraction,h, is the half heighth of the flute, a is the degrees spread, a,arr/360, a, ASN[SlN(d )/N,], a ATN[SIN(a,)]/[N, COS(a,)], and a, a, a

8. In an aspheric lens which produces paths of light parallel to itsoptical axis from the rays of light passing therethrough with theemitted light being concentrated and having minimal chromaticaberration, said lens having a frontal surface and a back surface, saidfrontal surface being substantially planar, and a fresnel-type asphericcurvature being formed on the entire active area of said back surface,said fresnel-type aspheric curvature being defined in the X-Y coordinatesystem y ={YI[TAN(A3)I HI 1)]l/ a) COT(A,)] and B, =X,+(C,Y,)[TAN(A;,)]wherein N, is the index of refraction, F, is the focal distance to saidback surface, X, is the variable X, Y, is the variable Y, H, is theheighth, K, is the limit of active surface, A, ATN(H 1/ 1) 3 ATN I MJ/[F MOIL B, X value of point being calculated; and C, Y of value of pointbeing calculated.

9. An aspheric lens as set forth in claim 8 wherein said curvature isfurther defined by V, which is a vertical riser limiting depth wherebythe curvature continues until the V, depth is reached aNd then shifts toits plane of origin aNd restarts until V, is again reached until thecurve is completed;

g 7 UNITED STATES PATEN OFFICE- CERTIFICATE OF CORRECTION Patent No. 35742386 M HOWARD A. SCI-IAEFER Inventofls) It is certified that errorappears in the above-identified patent and that said Letters Patent arehereby corrected as shown below:

Column 3, line 60, "11 should be CO ]Y UH1IT '6 1i-I 1e s end 5 "(1 1/311 v Shoojlld be 1.i"" o Column 7, line 8 ,"haVin g" should be having"Column 8 T11 155 I Q115 "0.5 should be I Q 5 column 8, line 10, "ATN["should be ATN- co ma, lame 10, "(a 1", should be (61 M) I Column 8, line"(3 4) 11' shoold be Column 8, line 31, "arid" should be and 051m 8,line 32, f'ana" should be and Signed and sealed this 15th day of October1974.

(SEAL) Attest:

MCCOY M. GIBSON JR. c. MARSHALL 'DANN Attesting Office: T Commissionerof Patents

1. A light transmitting lens comprising a lens body having a frontal surface and a back surface, said back surface being substantially planar, a plurality of parallel flutes formed in a generally circular area on said back surface to diverge the rays of light away from the axis of the lens to thereby create an auxiliary spread light, a fresnel-type curvature being disposed in said circular area at the top edge of the active area of the back surface transverse the direction of said parallel flutes to direct the rays of light downward toward the axis of the lens, said fresnel-type curvature being formed from an aspheric curvature, said aspheric curvature being a smooth curve of constantly changing radius said generally circular area is ring shaped, said frontal surface is non-planar and said frontal surface has an aspheric curvature which is a smooth curve with constantly changing radius.
 2. A light transmitting lens for a housing having an open end with a light source in the housing disposed remote from the open end, said lens having mounting means for closing the open end of said housing from its surrounding environment, said lens having a back surface for being disposed within the housing and a frontal surface for being disposed in the environment outside the housing, said frontal surface being planar, the entire active area of said back surface having a fresnel-type curvature with concentric ridges, said fresnel-type curvature being formed from a non-hyperboloid aspheric curvature, and said aspheric curvature being of smooth curve of constantly changing radius with the points on the curve being constantly recalculated in accordance with the focal distance to the face of the back surface, in accordance with the index of refraction of the lens and in accordance with the vertical riser limiting depth to create a uniform concentrated beam of parallel rays.
 3. An aspheric lens as set forth in claim 2 in combination with a light source, and said back surface being disposed between said front surface and said light source.
 4. An aspheric lens as set forth in claim 3 including a housing having an open end, said lens closing said open end to seal said housing, and said light source being in said housing.
 5. In an aspheric lens which produces paths of light parallel to its optical axis from the rays of light passing therethrough with the emitted light being concentrated and haVing minimal chromatic aberration, said lens having a frontal surface and a back surface, at least a portion of said back surface having a fresnel-type aspheric curvature; said frontal surface having an aspheric curvature, said back surface being substantially planar, and a plurality of parallel flutes being formed in a portion of said back surface to provide an auxiliary spread light pattern, said flutes being arranged in a substantially ring shaped area, said fresnel-type curvature being in a portion of said area, and said flutes being disposed substantially normal to said fresnel-tYpe curvature, said aspheric curvature on said frontal surface being defined in the X-Y coordinate system by B1 being equal to (X1(COT(A6) ) + Y1- J1 + D1(TAN(A4) ))/(TAN(A4) + COT(A6) ) and C1 being equal to J1 + (B1 - D1) (TAN(A4) ) wherein N1 is the index of refraction, H1 is the heighth, X1 is the X value of the previous calculated point, Y1 is Y value of the previous calculated point, F1 is the focal distance from the focal point to said back surface, R1 is the radius of the back surface, G1 4(2R1F1 + F12) , A1 ATN (H1/F1), E1 2(R1+ F1) (COS(A1)), E2 E12 - G1, M5 (E1 - Square Root E2) (0.5), J1 M5(SIN(A1)), D1 (J1 - H1) (TAN(A1)), A2 ASN (J1/R1), A7 A1 + A2, A3 ASN(SIN(A7)/N1), A4 A3 - A2, A5 ATN (SIN(A4)/(N1 - COS(A4) )), A6 A4 + A5, B1 X value of point being calculated; and C1 Y value of point being calculated.
 6. An aspheric lens as set forth in claim 5 wherein saId fresnel-type aspheric curvature is defined in the same manner as said frontal surface aspheric curvature.
 7. An aspheric lens as set forth in claim 6 wherein each of said flutes is defined in cross-section by a radius r1 h1/SIN(a4) and a chord heighth h2 ( r1 - 0.5 Square Root +(r1)2 - (2h1)2 ), wherein N1 is the index of refraction, h1 is the half heighth of the flute, a is the degrees spread, a1 a pi /360, a2 ASN(SIN(a1)/N1), a3 ATN(SIN(a2)) /(N1 - COS(a2)), and a4 a2 + a3.
 8. In an aspheric lens which produces paths of light parallel to its optical axis from the rays of light passing therethrough with the emitted light being concentrated and having minimal chromatic aberration, said lens having a frontal surface and a back surface, said frontal surface being substantially planar, and a fresnel-type aspheric curvature being formed on the entire active area of said back surface, said fresnel-type aspheric curvature being defined in the X-Y coordinate system by C1 ( Y1(TAN(A3))-H1 (COT(A1))) (TAN(A3) - COT(A1)) and B1 X1+(C1- Y1)(TAN(A3)) wherein N1 is the index of refraction, F1 is the focal distance to said back surface, X1 is the variable X, Y1 is the variable Y, H1 is the heighth, K1 is the limit of active surface, A1 ATN(H1/F1), A3 ATN ((SIN(A1)/(N1-COS(A1))), B1 X value of point being calculated; and C1 Y of value of point being calculated.
 9. An aspheric lens as set forth in claim 8 wherein said curvature is further defined by V1 which is a vertical riser limiting depth whereby the curvature continues until the V1 depth is reachEd and then shifts to its plane of origin and restarts until V1 is again reached until the curve is completed. 